SOLUTION: I need your help to solve this problem A hotel administrator has 200 rooms available for rent each night. Experience shows that if he charges $45 per night, he will have full

Question 44396: I need your help to solve this problem
A hotel administrator has 200 rooms available for rent each night. Experience shows that if he charges $45 per night, he will have full occupancy, but that for each $5 that he increases the price, 4 rooms become vacant. All other factors being equal, what will his maximum revenue be?
A. $16,820
B. $13,520
C. $8820
D. $12,000
E. $11,520
F. $18,000
G. none of these

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let "x" be the number of $5 increases.
Then Revenue = (45+5x)(200-4x)
= 45(200)+1000x-180x-20x^2
= -20x^2+820x+9000
Maximum Revenue occurs when
x=-b/2a =-(820)/-40=20.5
When x=20.5, Revenue = $17405
Cheers,
Stan H.
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